Nonlinear Least-squares Regression Research Articles

Experimental and analytical investigation of water diffusion process in nano-carbon/alumina/silica filled epoxy nanocomposites

This study discusses the water absorption behavior of three different types of nanocomposites. Silica, carbon and alumina nanoparticles are used as fillers incorporated in epoxy resin with different contents of 0.5, 1.5, and 3 wt%. A new nonlinear least-squares regression approach in conjunction with a gradient optimization was developed using symbolic manipulator MAPLE software to find the best fit. The equilibrium moisture content of the nanocomposites is measured as a function of time and the analytical modelling is successfully conducted. Results indicate that the addition of nanoparticles generally lower moisture content in contrast to neat epoxy. Compositions of 1.5 and 3 wt% alumina as well as silica nanocomposites however show a different behaviour. Diffusion coefficients for different types of nanocomposites were computed using Fickian and Langmuir models of diffusion. The least and highest diffusion coefficients correspond to the addition of silica 0.5 wt% and alumina 3 wt%, respectively.

Goodness of fit to a mathematical model for Drosophila sleep behavior is reduced in hyposomnolent mutants.

The conserved nature of sleep in Drosophila has allowed the fruit fly to emerge in the last decade as a powerful model organism in which to study sleep. Recent sleep studies in Drosophila have focused on the discovery and characterization of hyposomnolent mutants. One common feature of these animals is a change in sleep architecture: sleep bout count tends to be greater, and sleep bout length lower, in hyposomnolent mutants. I propose a mathematical model, produced by least-squares nonlinear regression to fit the form Y = aX∧b, which can explain sleep behavior in the healthy animal as well as previously-reported changes in total sleep and sleep architecture in hyposomnolent mutants. This model, fit to sleep data, yields coefficient of determination R squared, which describes goodness of fit. R squared is lower, as compared to control, in hyposomnolent mutants insomniac and fumin. My findings raise the possibility that low R squared is a feature of all hyposomnolent mutants, not just insomniac and fumin. If this were the case, R squared could emerge as a novel means by which sleep researchers might assess sleep dysfunction.

Nine-Lump Kinetic Study of Catalytic Pyrolysis of Gas Oils Derived from Canadian Synthetic Crude Oil

Catalytic pyrolysis of gas oils derived from Canadian synthetic crude oil on a kind of zeolite catalyst was conducted in a confined fluidized bed reactor for the production of light olefins. The overall reactants and products were classified into nine species, and a nine-lump kinetic model was proposed to describe the reactions based on appropriate assumptions. This kinetic model had 24 rate constants and a catalyst deactivation constant. The kinetic constants at 620°C, 640°C, 660°C, and 680°C were estimated by means of nonlinear least-square regression method. Preexponential factors and apparent activation energies were then calculated according to the Arrhenius equation. The apparent activation energies of the three feed lumps were lower than those of the intermediate product lumps. The nine-lump kinetic model showed good calculation precision and the calculated yields were close to the experimental ones.

The dissociation constants of the cytostatic bosutinib by nonlinear least-squares regression of multiwavelength spectrophotometric and potentiometric pH-titration data

Potentiometric and spectrophotometric pH-titration of the multiprotic cytostatics bosutinib for dissociation constants determination were compared. Bosutinib treats patients with positive chronic myeloid leukemia. Bosutinib exhibits four protonatable sites in a pH range from 2 to 11, where two pK are well separated (ΔpK>3), while the other two are near dissociation constants. In the neutral medium, bosutinib occurs in the slightly water soluble form LH that can be protonated to the soluble cation LH43+. The molecule LH can be dissociated to still difficultly soluble anion L−. The set of spectra upon pH from 2 to 11 in the 239.3–375.0nm was divided into two absorption bands: the first one from 239.3 to 290.5nm and the second from 312.3 to 375.0nm, which differ in sensitivity of chromophores to a pH change. Estimates of pK of the entire set of spectra were compared with those of both absorption bands. Due to limited solubility of bosutinib the protonation in a mixed aqueous-methanolic medium was studied. In low methanol content of 3–6% three dissociation constants can be reliably determined with SPECFIT/32 and SQUAD(84) and after extrapolation to zero content of methanol they lead to pKc1=3.43(12), pKc2=4.54(10), pKc3=7.56(07) and pKc4=11.04(05) at 25°C and pKc1=3.44(06), pKc2=5.03(08) pKc3=7.33(05) and pKc4=10.92(06) at 37°C. With an increasing content of methanol in solvent the dissociation of bosutinib is suppressed and the percentage of LH32+ decreases and LH prevails. From the potentiometric pH-titration at 25°C the concentration dissociation constants were estimated with ESAB pKc1=3.51(02), pKc2=4.37(02), pKc3=7.97(02) and pKc4=11.05(03) and with HYPERQUAD: pKc1=3.29(12), pKc2=4.24(10), pKc3=7.95(07) and pKc4=11.29(05).

Effect of acid washing on pyrolysis of Cladophora socialis alga in microtubing reactor

Cladophora socialis is a unique macroalga that is widely grown in the coastal regions of Vietnam. In this work, the pyrolysis characteristics of C. socialis were evaluated using thermogravimetric analysis (TGA) and pyrolysis in a tubing reactor. Macroalgae have a high content of inorganic compounds. These compounds result in high char content during pyrolysis of the macroalgae, which degrades the quality of the product bio-oil. In order to study this effect, C. socialis was demineralized by acid washing to remove the inorganic compounds. The effect of acid washing on the pyrolysis product distribution and the selectivity of composition in pyrolysis oil was carefully investigated. The kinetic parameters and the primary reaction pathways were also determined based on experimental data using nonlinear least-squares regression assuming a first-order kinetics model.

Kinetic modeling of catalytic cracking of C4 alkanes over La/HZSM-5 catalysts in light olefin production

Kinetic modeling of catalytic cracking (CC) of C4 alkanes (mixture of i-butane and n-butane), over Lanthanum modified HZSM-5 catalyst has been studied at 582–630°C in a plug flow reactor. The elementary reaction steps, i.e., protolytic cracking (PC) of CC and CH bonds in alkane molecules, hydrogen transfer between butane and light olefins, olefin cracking, β-scission, adsorption and desorption were taken into account. The combination of theory of reaction routes and LHHW has been employed in the complicated CC network to drive explicit overall reaction rate of reactantand product molecules. Then, the parameter estimation and model discrimination were performed based on the minimization of mean residual sum of squares between experimental and theoretical rates. The intrinsic kinetic parameters were estimated by non-linear least-square regression using MATLAB optimization toolbox.

On the spatial decorrelation of stochastic solar resource variability at long timescales

Understanding the spatial and temporal characteristics of solar resource variability is important because it helps inform the discussion surrounding the merits of geographic dispersion and subsequent electrical interconnection of photovoltaics as part of a portfolio of future solutions for coping with this variability. Unpredictable resource variability arising from the stochastic nature of meteorological phenomena (from the passage of clouds to the movement of weather systems) is of most concern for achieving high PV penetration because unlike the passage of seasons or the shift from day to night, the uncertainty makes planning a challenge. A suitable proxy for unpredictable solar resource variability at any given location is the series of variations in the clearness index from one time period to the next because the clearness index is largely independent of the predictable influence of solar geometry. At timescales shorter than one day, the correlation between these variations in clearness index at pairs of distinct geographic locations decreases with spatial extent and with timescale. As the aggregate variability across N decorrelated locations decreases as 1/√N, identifying the distance required to achieve this decorrelation is critical to quantifying the expected reduction in variability from geographic dispersion.Using 10years of satellite-derived daily-interval solar resource data across the world, we demonstrate that the spatiotemporal behavior of unpredictable solar resource variability is mirrored at longer timescales. We do so by examining over 1.4 million unique pairs of sites across the Western hemisphere and quantifying the influence each pair’s geographic separation and bearing has on the correlation between the variability of each pair’s clearness indices at timescales of one, two, four, seven, fifteen and thirty days. Expected pair-decorrelation distances are estimated by fitting exponential trends to the data using nonlinear least-squares regression and are presented as a function of timescale and pair orientation.Reflecting the predominant direction in which meteorological phenomena propagate at each of these timescales, we find that pairs of sites require considerably shorter distances to decorrelate when they are oriented north to south versus when they are oriented east to west. As at shorter timescales, these decorrelation distances are shown to increase with both timescale and with geographic extent.

The stability of tryptophan, 5-methyl-tryptophan and α-methyl-tryptophan during NaOH hydrolysis of selected foods

This study evaluated the use of 5-methyl-tryptophan, α-methyl-tryptophan or synthetic tryptophan to correct for the losses of protein-bound tryptophan in foods during NaOH hydrolysis. Synthetic tryptophan and each protein source was incubated in 4.5M NaOH containing 5-methyl-tryptophan and α-methyl-tryptophan in nitrogen gas-sparged Teflon vials for 0–144h at 110°C. The hydrolysis and loss rates of protein-bound tryptophan, 5-methyl-tryptophan, α-methyl-tryptophan and synthetic tryptophan were predicted using least-squares nonlinear regression. Using 5-methyl-tryptophan or synthetic tryptophan to correct for hydrolytic losses of tryptophan overestimated the tryptophan content by 8.2–19% and −0.3–8.8% respectively, while correction using α-methyl-tryptophan underestimated tryptophan by between 0.2% and 8.1% across the protein sources. Correction using α-methyl-tryptophan or synthetic tryptophan was more accurate than using 5-methyl-tryptophan, but when highly accurate tryptophan composition data are required, least-squares nonlinear regression is the best approach as it removes the need for a hydrolysis correction factor.

Measurement and Modeling for Isobaric Vapor–Liquid Equilibrium of Binary 1,3,5-Trichlorobenzene + 3,5-Dichloroaniline and 3-Chloroaniline + 3,5-Dichloroaniline Systems

The isobaric vapor–liquid equilibrium data for binary systems of 1,3,5-trichlorobenzene (1) + 3,5-dichloroaniline (2) and 3-chloroaniline (1) + 3,5-dichloroaniline (2) were measured experimentally under pressures of 20.00, 60.00 and 101.20 kPa using an inclined ebulliometer. Thermodynamic consistency of the vapor–liquid equilibrium data was tested by means of the Herington semiempirical method, and the isobaric vapor–liquid equilibrium data were correlated with three activity coefficient models, which were Wilson, NRTL and UNIQUAC. The energy interaction parameters were acquired by a nonlinear least-squares regression method for the three thermodynamic models. Results indicate that all the three activity coefficient models can describe the measured isobaric vapor–liquid data acceptably. The isobaric vapor–liquid equilibrium data determined in the present work are important in the design and operation for purification of 3,5-dichloroaniline by distillation.

Saturated vapor pressure of 4-fluorophthalic anhydride and 4-chlorophthalic anhydride and isobaric vapor–liquid phase equilibrium of 4-fluorophthalic anhydride + 4-chlorophthalic anhydride: Measurement and modeling

The saturated vapor pressures of 4-fluorophthalic anhydride and 4-chlorophthalic anhydride at various temperatures ranging from T=(426 to 560)K, and the isobaric vapor–liquid phase equilibrium data for binary system of 4-fluorophthalic anhydride (1)+4-chlorophthalic anhydride (2) at pressures of 21.33kPa, 41.33kPa, 61.33kPa and 81.33kPa were measured experimentally by means of an inclined ebulliometer. The relationship between saturated vapor pressure and temperature was fitted by using two Antoine equations and the Antoine constants were acquired for 4-fluorophthalic anhydride and 4-chlorophthalic anhydride, respectively. The semi-empirical method, Herington method was employed to test thermodynamic consistency of the vapor–liquid equilibrium data. The isobaric vapor–liquid phase equilibrium data were fitted with three thermodynamic models, which corresponded to Wilson, NRTL and UNIQUAC. The parameters of the three activity coefficient models were obtained by the method of nonlinear least-square regression. The calculated vapor–liquid phase equilibrium data with the three activity coefficient models agree very well with the experimental values.

Ternary Liquid–Liquid Equilibrium Data for the Water + Acetonitrile + {Butan-1-ol or 2-Methylpropan-1-ol} Systems at (303.2, 323.2, 343.2) K and 1 atm

Ternary liquid–liquid equilibrium (LLE) data were measured and correlated for the water + acetonitrile + (butan-1-ol or 2-methylpropan-1-ol) systems at (303.2, 323.2, and 343.2) K and 1 atm. A double-walled glass cell with the direct analytical method was used to measure the liquid–liquid equilibrium data. The phase equilibrium samples were analyzed and quantified using gas chromatography. The nonrandom two-liquid activity coefficient model was used to fit the experimental tie-lines using nonlinear least-squares regression of the data. Relative selectivity values for solvent separation efficiency were calculated from the tie-line data. The plait point for each temperature was estimated with the graphical Coolidge method.

Influence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element (FE) model for the Sutong cable-stayed bridge (SCB) is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.

An O−C (and light travel time) method suitable for application to large photometric databases

The standard method of studying period changes in variable stars is to study the timing residuals or O−C values of light-curve maxima or minima. The advent of photometric surveys for variability, covering large parts of the sky and stretching over years, has made available measurementsofprobablyhundredsofthousandsofvariablestars,observedatrandomphases. Simple methodology is described which can be used to quickly check such measurements of a star for indications of period changes. Effectively, the low-frequency periodogram of a first-order estimate of the O−C function is calculated. In the case of light travel time (LTT) effects, the projected orbital amplitude follows by robust regression of a sinusoid on the O−C. The results can be used as input into a full non-linear least-squares regression directly on the observations. Extensive simulations of LTT configurations are used to explore the sensitivity of results to various parameter values (period of the variable star and signal to noise of measurements; orbital period and amplitude; number and time baseline of observations). The methodology is applied to observations of three previously studied stars.

Personalized Oxycodone Dosing: Using Pharmacogenetic Testing and Clinical Pharmacokinetics to Reduce Toxicity Risk and Increase Effectiveness

To develop a framework for integrating pharmacogenetics with clinical pharmacokinetics for personalized oxycodone dosing based on a patient's CYP2D6 phenotype. Randomized, crossover, double-blind, placebo-controlled. Subjects were genotyped as CYP2D6 ultra-rapid metabolizer, extensive metabolizer, or poor metabolizer phenotypes. Five subjects from each phenotype were randomly selected for inclusion in our study. Studies were performed in silico. The subjects were male, age 26 years, height 181.2 cm, and weight 76.3 kg. They were healthy without comorbidities, and their medical examinations were normal. The trajectories of phenotype-specific plasma oxycodone concentration-time profiles were analyzed using weighted nonlinear least-squares regression with WinSAAM software. A global two-stage population-based model data analysis procedure was used to analyze the studies. Clinical pharmacokinetics were calculated using the R package cpk, eliminating the need to perform hand-calculations. Our study shows how clinicians can reduce risk and increase effectiveness for oxycodone dosing by (1) determining the patient's likely metabolic response through testing a patient's CYP2D6 phenotype, and (2) calculating clinical pharmacokinetics specific to the patient's CYP2D6 phenotype to design a personalized oxycodone dosing regimen. Personalized oxycodone dosing is a new tool for a clinician treating chronic pain patients requiring oxycodone. By expressing a patient's CYP2D6 phenotype pharmacokinetically, a clinician (at least theoretically) can improve the safety and efficacy of oxycodone and decrease the risk for iatrogenically induced overdose or death. Pharmacokinomics provides a general framework for the integration of pharmacogenetics with clinical pharmacokinetics into clinical practice for gene-based prescribing.

Vapor–Liquid Equilibrium Data for Binary Systems of n-Dodecane + {Propan-1-ol, Butan-1-ol, 2-Methylpropan-1-ol} at 40 kPa

Isobaric (T–x–y) binary vapor–liquid equilibrium (VLE) data were measured and modeled for the n-dodecane + {propan-1-ol, butan-1-ol, or 2-methylpropan-1-ol} systems at 40 kPa. A low pressure dynamic still, capable of measuring systems of high relative volatility, was used for the measurements. The vapor and liquid equilibrium compositions were determined using a gas chromatograph with a thermal conductivity detector. The experimental data were regressed using the combined method (γ–φ approach). The nonrandom two-liquid (NRTL) activity coefficient model was used to describe the liquid phase nonideality, and the vapor phase was assumed to be ideal. The NRTL model parameters were determined using nonlinear least-squares regression. The experimental data were found to be well correlated with the thermodynamic modeling. No azeotropic behavior has been observed. The three investigated systems show a large positive deviation from Raoult’s law.

Market value of R&D, patents, and organizational capital: Finnish evidence

This paper studies how knowledge and organizational capital (OC) affect the market valuation of firms. Detailed occupational information from Finnish linked employer–employee data is used to form new estimates of firms’ organizational investments. The market value of OC is analyzed together with research and development (R&D) and patent variables. A nonlinear least-squares regression is used to investigate the contribution of these variables to the market value of Finnish firms during the period 1995–2008. The results show that OC, R&D, patents, and patent citations all have positive and significant effects on market value. A particularly interesting finding is that the effect of OC appears to be even stronger than the effect of R&D investments. This study also provides internationally comparable results on the market valuation of knowledge assets that indicate that in Finland, the market valuation of R&D, but not patents, is lower than in the USA and many European countries.

Vapor pressure and isobaric vapor–liquid equilibrium for dichloronitrobenzene isomers

The saturated vapor pressures of pure 3,4-dichloronitrobenzene and 2,3-dichloronitrobenzene and the isobaric vapor–liquid equilibrium (VLE) data for binary 3,4-dichloronitrobenzene+2,3-dichloronitrobenzene system under 20.00kPa, 60.00kPa and 101.30kPa were measured experimentally using an inclined ebulliometer. The saturated vapor pressure was correlated by an Antoine equation. Thermodynamic consistency of the vapor–liquid equilibrium data was tested by means of Herington semi-empirical method, and the vapor–liquid equilibrium data were correlated with Wilson, NRTL and UNIQUAC activity coefficient models. The parameters of the three thermodynamic models were obtained by a nonlinear least-square regression method. All the three models can describe the measured vapor–liquid data satisfactorily. The vapor pressures and the vapor–liquid equilibrium data presented in the paper are essential for the design and operation for separation of the isomeric mixture of 3,4-dichloronitrobenzene+2,3-dichloronitrobenzene via distillation.

Maximum-Likelihood Estimation for Indicator Dilution Analysis

Indicator-dilution methods are widely used by many medical imaging techniques and by dye-, lithium-, and thermodilution measurements. The measured indicator dilution curves are typically fitted by a mathematical model to estimate the hemodynamic parameters of interest. This paper presents a new maximum-likelihood algorithm for parameter estimation, where indicator dilution curves are considered as the histogram of underlying transit-time distribution. Apart from a general description of the algorithm, semianalytical solutions are provided for three well-known indicator dilution models. An adaptation of the algorithm is also introduced to cope with indicator recirculation. In simulations as well as in experimental data obtained by dynamic contrast-enhanced ultrasound imaging, the proposed algorithm shows a superior parameter estimation accuracy over nonlinear least-squares regression. The feasibility of the algorithm for use in vivo is evaluated using dynamic contrast-enhanced ultrasound recordings obtained with the purpose of prostate cancer detection. The proposed algorithm shows an improved ability (increase in receiver-operating characteristic curve area of up to 0.13) with respect to existing methods to differentiate between healthy tissue and cancer.

Functional response of the phytoseiid mite Typhlodromus negevi Swirski and Amitai to the two-spotted spider mite Tetranychus urticae (Acari: Tetranychidae)

The functional response of the predator Typhlodromus negevi Swirski and Amitai fed on nymphal stages of Tetranychus urticae Koch was determined. A logistic regression of the proportion of prey consumed as a function of initial prey density to identify functional response types was conducted. Therefore, non-linear least-squares regression and the random predator equation to estimate attack rates and handling times were followed. Overall, all stages of T. negevi exhibited a type II functional response to T. urticae. Whereas, the attack rate (a) and handling time (Th) of protonymph, deutonymph, and female of T. negevi recorded as 0.0329 and 2.0313, 0.0934 and 1.7918, and 0.1068 and 1.0796 when offered nymphal stages of T. urticae, respectively.

A comparative study of the influence of shift factor equations on master curve construction

This paper evaluates the applicability of different shifting techniques for constructing complex modulus master curves using the time-temperature superposition principle (TTSP). A database of complex modulus results of unmodified bitumens, polymer modified bitumens (PMBs), bitumen-filler mastics, unaged and aged bitumens was used together with a Generalized Logistic Sigmoidal Model to assess the validity of seven different shifting approaches. Except for the Laboratoire Central des Ponts et Chaussees (LCPC) method, the construction of master curves was done using the Generalised Logistic Sigmoidal Model and non-linear least squares regression optimization with the aid of the Microsoft Excel Spreadsheet Solver function. The goodness-of-fit for the various shifting techniques and functions was assessed through graphical and statistical methods. From the study, it was found that a numerical shift approach using non-linear least squares produced the best fit between experimental and predicted data in terms of both graphical and goodness-of-fit statistics. The ranking of the other shifting techniques consisted of the LCPC approach, followed by the William, Landel and Ferry (WLF), Modified Kaelble, Viscosity Temperature Susceptibility (VTS), Arrhenius and Log-Linear methods. However, most of the equations are basically empirical and they are not expected to be strictly obeyed by any materials. Discrepancies were still evident, even for the better functions, for those materials that demonstrated a deviation from the thermorheological simplicity of the rheological behaviour as found for highly structured bitumens following high degrees of polymer modification and/or oxidative ageing.